Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
![### Simplifying Algebraic Expressions: Step-by-Step Guide
In this example, we'll walk through the process of simplifying an algebraic expression involving distribution and combining like terms.
#### Original Equation:
\[ 6(2x + 5) - 3(x + 4) \]
#### Step-by-Step Solution:
1. **Distribute (Expand) the Expression:**
- Apply the distributive property to each term inside the parentheses.
\[ 6(2x + 5) \rightarrow 12x + 30 \]
\[ -3(x + 4) \rightarrow -3x - 12 \]
2. **Rewrite the Expanded Expression:**
\[ 12x + 30 - 3x - 12 \]
3. **Combine Like Terms:**
- Combine the \( x \)-terms \((12x - 3x)\):
\[ 12x - 3x = 9x \]
- Combine the constant terms \((30 - 12)\):
\[ 30 - 12 = 18 \]
4. **Simplified Expression:**
\[ 9x + 18 \]
By following these steps, we've simplified the expression from \( 6(2x + 5) - 3(x + 4) \) to \( 9x + 18 \). This process includes distributing, rewriting, and combining like terms to achieve the final simplified form.
### Diagram Description:
- There are arrows indicating the steps of distribution.
- Each part of the expression is clearly shown being multiplied and then simplified step by step.
- This visual representation helps in understanding the application of the distributive property and combining like terms.
This example will help you simplify similar algebraic expressions by applying these fundamental algebraic concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8013d441-5946-4d9d-b85b-992de95a8487%2F35005fc0-234f-46a5-9d70-dd14c0c142df%2Fsadk854_processed.jpeg&w=3840&q=75)
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